Birefringent optical responses of single-chirality carbon nanotube membranes

Membranes composed of single-walled carbon nanotubes (SWCNTs) with a specific chiral structure (chirality) possess unique optical properties dominated by thermally robust quasi-one-dimensional excitons. Therefore they have emerged as promising materials for photonic and/or thermo-optic applications. As SWCNTs in the membranes are usually aligned two-dimensionally in a plane, and the optical responses of individual SWCNTs are highly anisotropic, the macroscopic responses of membranes are expected to depend on the light-propagation direction. However, the complex refractive-index spectra of some membrane axes are unknown, hindering the optical design of SWCNT-based devices that respond to arbitrarily propagating light. Here, we report the anisotropic complex refractive index spectra of a single-chirality SWCNT membrane fabricated via vacuum filtration. The polarization- and angle-resolved reflection spectra were obtained in the near-infrared-to-visible region. All spectral features in different polarizations and incident angle configurations were consistent with a uniaxial birefringent membrane, reflecting the random in-plane orientations of the SWCNTs. The ordinary (in-plane) refractive index spectra presented a series of sharp resonances of parallel-polarized excitons. The extraordinary (out-of-plane) refractive index in the 0.8–2.4 eV range was determined as ∼1.9. The extraordinary spectra included small but indispensable contributions from the cross-polarized exciton resonance, which are necessary for properly predicting the angle-dependent optical responses of the membrane. By completely unveiling the birefringent optical responses of single-chirality SWCNT membranes, this work paves the way for integrating SWNCT membranes into precise and diverse photonic and/or thermo-optic devices.